Solve: 5 1/3-3 5/6
5 1/3-3 5/6
5 1/3 = 4 5/3 = 4 10/6
4 10/6 - 3 5/6 = ?
To solve the expression 5 1/3 - 3 5/6, we need to subtract these mixed fractions.
Step 1: Convert the mixed fractions to improper fractions.
To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator. Write the sum over the denominator.
For the first mixed fraction:
5 1/3 = (5 * 3 + 1) / 3 = 16/3
For the second mixed fraction:
3 5/6 = (3 * 6 + 5) / 6 = 23/6
So the expression becomes 16/3 - 23/6.
Step 2: Find a common denominator.
To subtract fractions, we need a common denominator. The least common multiple (LCM) of 3 and 6 is 6, so we'll use 6 as the common denominator for both fractions.
Step 3: Rewrite the fractions with the common denominator.
To rewrite the fractions with the common denominator, we'll multiply the numerator and denominator of each fraction by the appropriate factor to make the denominators equal to 6.
16/3 = (16 * 2) / (3 * 2) = 32/6
23/6 remains the same.
So the expression is now 32/6 - 23/6.
Step 4: Subtract the fractions.
To subtract the fractions, we subtract the numerators and keep the common denominator.
32/6 - 23/6 = (32 - 23) / 6 = 9/6
Step 5: Simplify the fraction.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3 in this case.
9/6 divided by 3/3 = (9/6) * (1/3) = 9/18 = 1/2
Therefore, 5 1/3 - 3 5/6 = 1/2